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How and when do you cover this topic?

Discussion in 'Mathematics' started by SMC21, Nov 26, 2011.

  1. Pupils are taught about the laws of indices, cancelling down, the importance of the equals sign when manipulating equations and of 'doing the same to both sides' of an equation.

    Also, in tackling problems a pupil may have solved problems where he/she has equated two different expressions for volumes/areas and cancelled pi and r from both sides.

    So, for the following type of problem:

    n^2=3n

    a pupil may decide it is okay to divide both sides by n to get n=3

    or, for

    n(n-1)=0

    divide both sides by n to get n-1=0 so n=1

    and hence miss a solution each time.

    I am interested to know how, and at what stage, others highlight this particular aspect of solving equations.

    Also, do you know of any especially relevant resources/questions?

    Thank you :)
     
  2. Nazard

    Nazard New commenter

    I hadn't thought of this one before (and I know this isn't what you are asking about), but if you then divide both sides by (n-1) you rather neatly get 1 = 0

    I am afraid that this is a topic area I don't lay the groundwork for when the pupils are younger and probably should.

    For example, when solving quadratics (either using factorising or the formula) I am careful to talk about certain examples needing new techniques to provide a solution (when b^2-4ac is negative), rather than them being 'impossible' to solve. I don't, when encouraging pupils to 'do the same to both sides' urge caution when dividing by expressions - and probably should.

    Maybe we should start with the graph. This makes it significantly simpler to spot multiple solutions. But then the pupils who can currently solve 3x + 2 = 5x + 8 would need to be able to imagine the graphs of y = 3x+2 and y = 5x+8 and suss out where they would cross. This feels unlikely for many Yr 7/8 pupils. But then I suspect that those pupils probably won't meet as many quadratics as the pupils who _would_ cope with them.

    Hmm - will need to think further about this! I'll be interested to read other people's thoughts on this thread...
     
  3. LiamD

    LiamD New commenter

    I use Autograph so pupils can see that there is more than one solution. I then ask them to find an explanation for the missing solutions. It soon becomes clear where the omission has arisen.
    Then I threaten them with all manner of inventive punishments for future transgressions[​IMG].
     
  4. DM

    DM New commenter

    Surely this is enough of an incentive to be vigilant?
    [​IMG]
     
  5. Introduce the joke proof that 2 * 2 = 5, and see if someone susses out that it relies on a hidden divide by zero.

     

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